Elsevier

Journal of Symbolic Computation

Volume 58, November 2013, Pages 99-102
Journal of Symbolic Computation

Corrigendum to “Rational rotation-minimizing frames on polynomial space curves of arbitrary degree” [J. Symbolic Comput. 45 (8) (2010) 844–856]

https://doi.org/10.1016/j.jsc.2013.05.010
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Abstract

The existence of rational rotation-minimizing frames on polynomial space curves is characterized by the satisfaction of a certain identity among rational functions. Part 2 of Remark 5.1 in the original paper states an inequality among the degrees of the denominators of these rational functions, but the proof given therein was incomplete. A formal proof of this inequality, which is essential to the complete categorization of rational rotation-minimizing frames on polynomial space curves, appears to be a rather formidable task. Since all known examples and special cases suggest that the inequality is correct, it is restated here as a conjecture rather than a definitive result, and some preliminary steps towards the proof are presented.

Keywords

Rotation-minimizing frames
Pythagorean-hodograph curves
Spatial motion planning
Quaternions
Polynomial identities

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